Modified cosmology through generalized mass-to-horizon entropy: observational constraints from DESI DR2 BAO data

A generalized mass-to-horizon entropy has recently been proposed as an extension of the Bekenstein-Hawking area law, derived from a modified mass-horizon relation constructed to ensure consistency with the Clausius equation. Within the gravity-thermodynamics conjecture, this entropy formulation yields modified Friedmann equations, which recover the standard $\Lambda$CDM cosmology in the appropriate limit of the model's two free parameters. In the present study, we constrain this framework using observations from TypeIa supernovae (SNIa), cosmic chronometers (CC) and baryon acoustic oscillations (BAO, including DESI~DR2), together with the SH0ES distance-ladder prior on $H_0$, across four combinations of data sets. Although the extended entropic scenario yields a slightly better, or statistically comparable, fit to the data, model selection via the Akaike Information Criterion (AIC) mildly favors the cosmological constant as the dark energy candidate. Moreover, the $\Lambda$CDM limit lies within $\sim 1\sigma$ of our constraints, indicating no significant deviation from standard cosmology with current data.